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Symmetry of E and B, cont.
Section 23.1
Electromagnetic Waves
• Self-sustaining oscillations involving E and B are
possible
• The oscillations are an electromagnetic wave
• Electromagnetic waves are also referred to as
electromagnetic radiation
• Both the electric and magnetic fields must be
changing with time
• Although Maxwell worked out the details of em
waves in great mathematical detail, experimental
proof of the existence of the waves wasn’t carried
out until 1887
Section 23.1
EM Waves are Transverse Waves
• Imagine a snapshot of the electromagnetic wave
• The electric field is along the x-axis
• The wave travels in the z-direction
• Æ E x B, vector cross product
• Determined by the right-hand rule #2
• The magnetic field is along the y-direction
• Because both fields are perpendicular to the direction of
propagation, the wave is a transverse wave
Section 23.2
Light is an EM Wave
• Maxwell found the speed of an EM wave can be
expressed in terms of two universal constants
• Permittivity of free space, εo
• Magnetic permeability of free space, μo
• The speed of an EM wave is called c
c=
1
ε o μo
• Inserting the values, c = 3.00 x 108 m/s
• The value of the speed of an electromagnetic wave is
the same as the speed of light
Section 23.2
EM Waves in Material Substances
• When an em wave travels through a material
substance, its speed depends on the properties of
the substance. Density of electrons, which interact
with the wave and slow it down
• The speed of the wave, in “non-vacuum” is always
less than c
• The speed of the wave depends on the wave’s
frequency – because the atomic electrons elastically
bound in atoms have resonant frequencies. For
frequencies near resonance, the EM wave is slowed
down even more.
• Dispersion – waves of different freq. get out of step
Section 23.2
EM Waves Carry Energy
• An em wave carries
energy in the electric
and magnetic fields
associated with the
wave
Section 23.3
EM Waves Carry Energy, cont.
• The total energy per unit volume in the EM wave is
the sum of its electric and magnetic energies
• utotal = uelec + umag
uelec
1
1 2
2
= ε o E and umag =
B
2
2 μo
Section 23.3
EM Waves Carry Energy, final
• The electric and magnetic energies are equal and
this leads to the proportionality between the peak
electric and magnetic fields
1
1 2
2
ε o Eo =
Bo
2
2 μo
Eo = c Bo
• Remember F = qE = q v X B so it’s pretty natural to
find that E = cB since c is a velocity, (and a very
special velocity.)
Section 23.3
Intensity of an EM Wave
• The strength of an em wave is usually measured in
terms of its (energy) intensity
• SI unit is W/m2
• Intensity is the amount of energy transported per
second across a surface of area one square meter.
• Intensity also equals the energy density (per unit
volume) multiplied by the speed of the wave
• I = utotal × c = ½ εo c Eo2
• Since E = c B, the intensity is, equivalently,
proportional to the square of the magnetic field
amplitude
Section 23.3
Solar Cells
• The intensity of sunlight on a typical sunny day is
•
•
•
•
about 1000 W/m²
A solar cell converts the energy from sunlight into
electrical energy
Current photovoltaic cells capture only about 15% of
the energy that strikes them
Also must account for nights and cloudy days
Making better and more practical solar cells is an
important engineering challenge. Purdue is a center
of intense research on this, with a large
interdisciplinary team involved.
Section 23.3
EM Waves Carry Momentum
• An electromagnetic wave has
no mass, but it does carry
momentum p
• Photons have energy
E
E = pc
• Consider the collision of
photons (wave) with matter –
total absorption in this case
• The momentum is carried by
the wave before the collision
and by the matter after the
collision
Section 23.3
Radiation Pressure
• When an electromagnetic wave is absorbed by an
•
•
•
•
object, it exerts a force on the object, since it is
transferring momentum to the object
F = rate of change of p with time: “N2”
The total force on the object is proportional to its
exposed area: Energy/time = Intensity x Area
Radiation pressure is the radiation Force / Area
This can also be expressed in terms of the intensity
Pradiation
F I
= =
A c
Section 23.3
Electromagnetic Spectrum
• All em waves travel through a vacuum at the speed c
• c = 2.99792458 x 108 m/s ~ 3.00 x 108 m/s
• c is defined to have this value and the value of a meter
is derived from this speed –> 1m = distance travelled
in a certain fraction of a second.
• Electromagnetic waves are classified according to
their frequency and wavelength
• The wave equation applies to EM waves: c = ƒ λ
• The range of all possible electromagnetic waves is
called the electromagnetic spectrum
Section 23.4
EM Spectrum, Diagram
Visible is ~
one octave =
factor of 2 in f
Section 23.4
EM Spectrum, Notes
• There is no defined lower or upper limit for
electromagnetic wave frequencies
• The range of frequencies assigned to the different
types of waves is somewhat arbitrary
• Regions may overlap
• The names of the different regions were chosen
based on how the radiation in each frequency
interacts with matter and on how it is generated
Section 23.4
Radio Waves
• Frequencies from a few hertz up to about 109 hertz
• Corresponding wavelengths are from about 108
meters to a few centimeters
• Usually produced by an AC circuit attached to an
antenna
• A simple wire can function as an antenna
• Antennas containing multiple conducting elements or
shaped as “dishes” are usually more efficient and
more common
• Radio waves can be detected by an antenna similar
to the one used for emitting them
Radio Waves, cont.
• Parallel wires can act as an
•
•
•
•
antenna
The AC current in the antenna
is produced by time-varying
electric fields in the antenna
This then produces a timevarying magnetic field and the
EM wave
As the current oscillates with
time, the charges are
accelerated
In general, when an electric
charge is accelerated, it
produces electromagnetic
radiation
Section 23.4
Microwaves
• Microwaves have
frequencies between about
109 Hz and 1012 Hz
• Corresponding wavelengths
are from a few cm to a few
tenths of a mm
• Microwave ovens generate
radiation with a frequency
near 2.5 x 109 Hz
• The microwave energy is
transferred to water
molecules in the food,
heating the food
Section 23.4
Infrared
• Infrared radiation has
•
•
•
•
frequencies from about 1012
Hz to 4 x 1014 Hz
Wavelengths from a few
tenths of a mm to a few
microns
We sense this radiation as
heat
Blackbody radiation from
objects near room
temperature falls into this
range
Also useful for monitoring
the Earth’s atmosphere
Section 23.4
Visible Light
• Frequencies from about 4 x1014 Hz to 8 x1014 Hz
• Wavelengths from about 750 nm to 400 nm
• The color of the light varies with the frequency
• Low frequency; high wavelength – red
• High frequency; low wavelength – blue
• The speed of light inside a medium depends on the
frequency of the radiation
• The effect is called dispersion
•
White light is separated into different colors
Section 23.4
Dispersion Example
Section 23.4
Ultraviolet
• Ultraviolet (UV) light has frequencies from about 8 x
1014 Hz to 1017 Hz
• Corresponding wavelengths are about 400 nm to 3
nm
• UV radiation stimulates the production of vitamin D
in the body, also tanning
• Excessive exposures to UV light can cause sunburn,
skin cancer and cataracts
Section 23.4
X-Rays
• Frequencies from about 1017 Hz to about 1020 Hz
• Discovered by Wilhelm Röntgen in 1895
• X-rays are weakly absorbed by skin and other soft
tissue and strongly absorbed by dense material such
as bone, teeth, and metal
• X ray images of interior of body
• In the 1970’s CT (CAT) scans were developed – 3-D
imaging, but at the “cost” of unpleasantly high
radiation dosages to the patient – greater than a
year’s exposure to cosmic rays, radon, and other
natural radiation
Section 23.4
X-Ray Example
Section 23.4
CT Scan
• With a single X-ray image,
there will always be parts
of the person’s body that
are obscured
• Images can be taken from
different angles
• A CT scan takes many Xray images at many
different angles
• Computer analysis is used
to combine the images into
a three-dimensional
representation of the object
Section 23.4
Gamma Rays
• Gamma rays are the highest frequency
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•
•
•
electromagnetic waves, with frequencies above 1020
Hz
Wavelengths are less than 10-12 m
Gamma rays are produced by processes inside
atomic nuclei – changes in nuclear energy levels
One type of radioactive element decay. Including
decays of fission products produced in nuclear
power plants.
Gamma rays also reach us from outside the solar
system – one class of “Cosmic Rays””
Section 23.4
Astronomy and EM Radiation
• Different applications generally use different
wavelengths of em radiation
• Astronomy uses virtually all types of em radiation
• The pictures show the Crab Nebula at various
wavelengths
• (False) colors indicate intensity at various wavelengths
Section 23.4